An extension of the Kratzel function and associated inverse gaussian probability distribution occurring in reliability theory

International Journal of Computational and Mathematical Sciences

Volumn 3, Issue 4, 2009, Pages 189-198

  Saxena, R K ^a   Saxena, Ravi ^a  

^a JAI NARAIN VYAS UNIVERSITY   (India)

Author keywords

Bessel function of the third kind; Fox wright function; Inverse gaussian distribution; Kr tzel function

Indexed keywords

DIFFUSION PROCESS; GENERALIZED FUNCTIONS; GEOMETRIC FUNCTIONS; HAZARD RATES; INVERSE GAUSSIAN; INVERSE GAUSSIAN DISTRIBUTION; MELLIN TRANSFORM; MOMENT GENERATING FUNCTION; STATISTICAL FUNCTIONS; WRIGHT FUNCTIONS;

BESSEL FUNCTIONS; FUNCTION EVALUATION; GAUSSIAN DISTRIBUTION; HARMONIC ANALYSIS; PROBABILITY; QUALITY ASSURANCE; RELIABILITY ANALYSIS; RELIABILITY THEORY;

PROBABILITY DENSITY FUNCTION;

EID: 77949956547     PISSN: 20103905     EISSN: 20103913     Source Type: Journal    
DOI: None     Document Type: Article

References (30)

1. M. Abramowitz, and I. Stegun, Handbook of Mathematical Functions, Dover, New York, 1972.
2. I. Ali, S. L. Kalla and H. G. Khajah, "A generalized inverse Gaussian distribution with τ - confluent hypergeometric function", Integral Transforms Spec. Funct. 12, No.2, pp. 101-114, 2001.
3. B. Al-Saqabi, S. L. Kalla and R. Scherer, "On a generalized inverse Gaussian distribution", International Journal of Applied mathematics, 20, No.1,pp. 11-27, 2007.
4. M. A. Chaudhry, S. M. Zubair, "Generalized incomplete gamma functions with Applications", J. Comput. Appl. Math., 55, pp. 99-124, 1996.
5. M. A. Chaudhary, S. M. Zubair, "On the extension of generalized incomplete gamma function with applications", J. Aust. Math. Soc. Ser, B, 37, pp. 392-405, 1996.
6. R. S. Chinkara, and J. Leroy, Folks, The inverse Gaussian distribution: Theory, Methodology and Applications, Marcel Dekker, New York, 1989.
7. M. R. Dotsenko, On some applications of Wright's hypergeometric function, C. R. Acad. Bulgare Sci. 44, pp. 13-16, 199.
8. M. R. Dotsenko, On some applications of Wright's hypergeometric function, Mat. Fiz. Nelinein Mekh, No. 18 (52), pp. 47-52, 1993.
9. A. Erdėlyi, W. Magnus, F. Oberhettinger, and F. G.Tricomi, Higher Transcendental Functions, Vol. II, McGraw-Hill, New York-Toronto-London, 1953; Reprinted: Krieger, Melbourne, Florida, 1953, and 1981.
10. A. Erdėlyi, W. Magnus, F.Oberhettinger, and F. G. Tricomi, Tables of Integral Transforms, Vol. II, McGraw-Hill, New York-Toronto-London, 1954; Reprinted: Krieger, Melbourne, Florida, 1954, and 1981.
11. J. Good, The population frequencies of species and the estimation of population parameters, Biometrika, 40, pp. 237-260, 1953.
12. H. J. Haubold, and A. M. Mathai, "An integral arising frequently in astronomy and physics", SIAM Rev.40 (4), pp. 995-997, 1998.
13. J. N. Hoem, The statistical theory of demographic rates, Scand. J. Statist., 3, pp. 169-185, 1976.
14. B. Jorgensen, Statistical Properties of Generalized Inverse Gaussian Distributions, Lecture Notes in Statistics, 9, Springer, New York, 1982.
15. S. L. Kalla, B. N. Al-Saqabi, H. G. Khajah, "A unified form of gammatype distribution", Appl. Math. Comput. 118, No. 2-3, pp. 175-187, 2001.
16. A. A. Kilbas and M. Saigo, H-Transforms Theory and Applications, Chapman and Hall/ CRC, Roca Rotan, FL, New York, 2004.
17. A. A. Kilbas, R. K. Saxena, and Juan J. Trujillo, "Krätzel function as a function of.hypergeometric type", Frac. Calc. Appl. Anal. 9, pp. 109-131, 2006.
18. A. A. Kilbas, R. K. Saxena, Megumi Saigo, and Juan J. Trujillo, Generalized Wright function as the H-function In Analytic Methods of Analysis and Differential Equations, AMADE 2003, Cambridge Scientific Publishers, pp. 117-134, 2006.
19. E. Krätzel, Eine Verallgemeineirungder, Laplaceund Meijer - Transformation, Wiss. Z.Friedrich-Shiller -Univ. Mathnaturwiss.Reihe 14, No.5, pp. 369-381, 1965.
20. E. Krätzel, Integral transformation of Bessel type, In Generalized Functions and Operational Calculus (Proc. Conf. Varna, 1975. Bulg. Acad. Sci., Sofia, 1979), pp. 148-155, 1979.
21. A. M. Mathai, A Handbook of Special functions for Startistical and Physical Sciences, Clarendon Press, Oxford, 1993.
22. A. M. Mathai, and R. K. Saxena, The H-function with Applications in Statistics and Other Disciplines, Wilery, New York, 1978.
23. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives Theory and Applications, Gordon and Breach, Reading, 1993.
24. R. K. Saxena, On a unified inverse Gaussian distribution, to appear in the Proceedings of the 8th conference of Society for Special Functions and Their Applications held at Palai,Kerala, India, 2007.
25. R. K. Saxena and S. L. Kalla, On a generalization of Kratzel function and associated inverse Gaussian probability distributions, Algebras, Groups, and Geometries 24, pp. 303-324, 2007.
26. R. K. Saxena, A. M. Mathai and H. J. Haubold, Astrophysical thermonuclear functions for Boltzmann-Gibbs statistics and Tsallis statistics, Physica A 344, pp. 649-656, 2004.
27. N. Virchenko, "On some generalizations of the functions of hypergeometric type", Fract. Calc. Appl. Anal.2, No.3, pp. 233-244, 1999.
28. N. Virchenko, S. L. Kalla, and A. Al-Zamel, Some results on a generalized hypergeometric function, Integral Transform Spec. Funct. 12, No.1, pp. 89-100, 2001.
29. E. M. Wright, The asymptotic expansion of the generalized hypergeometric function, J. London Math. Soc.10, pp. 286-293, 1935.
30. E. M. Wright, The asymptotic expansion of the generalized hypergeometric function, Proc. London Math. Soc. (Ser.2), 46, pp. 389-408, 1940.